CN112082146B - Method for determining length of droplet evaporation section of temperature and pressure reducer for bypass heat supply of thermal power generating unit - Google Patents
Method for determining length of droplet evaporation section of temperature and pressure reducer for bypass heat supply of thermal power generating unit Download PDFInfo
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Abstract
The invention discloses a method for determining the length of a droplet evaporation section of a temperature and pressure reducer for bypass heat supply of a thermal power generating unit, which is characterized by comprising the following steps of: the method comprises the following steps: the method comprises the steps of selecting and constructing a physical model of a temperature and pressure reducer and a liquid drop evaporation section pipeline, calculating a three-dimensional flow area of the temperature and pressure reducer and the liquid drop evaporation section pipeline, performing regression orthogonal analysis on the temperature and pressure reducer and the liquid drop evaporation section pipeline, testing the significance and the instability of a regression equation and the like, and solves the problem that the length of a liquid drop evaporation section of the temperature and pressure reducer cannot be calculated in the transformation of a bypass heating system of the existing cogeneration unit. The method provides reliable theoretical guidance and construction standards for flexibility modification of the cogeneration unit, and fills the blank in the field of pipeline safety of the temperature and pressure reducing system in bypass heat supply modification. The method is scientific and reasonable, high in applicability, high in calculation precision and good in effect.
Description
Technical Field
The invention relates to the field of design, monitoring and diagnosis of bypass heating equipment in the process of deep peak shaving heating of a thermal power generating unit, in particular to a method for determining the length of a droplet evaporation section of a temperature and pressure reducer for bypass heating of the thermal power generating unit.
Background
In order to eliminate the 'thermoelectric constraint' influence of the cogeneration unit and improve the operation flexibility of the cogeneration unit. The bypass heating and high-low side combined heating of the cogeneration unit gradually become a new trend. The temperature and pressure reducer becomes the indispensable device of thermal power generating unit bypass heat supply steam flow transformation, reduces the temperature and steps down of realizing steam through throttle diffusion effect and water spray desuperheating to satisfy industrial steam or heating demand. The most split type temperature and pressure reduction ware that is of tradition temperature and pressure reduction ware makes steam pass through earlier multistage orifice plate step-down in the valve body, and the nozzle water spray temperature reduction cools down in the rethread temperature reduction ware, and nevertheless the temperature reduction pressure reduction effect is limited. In order to meet the requirement of bypass heat supply, a high-parameter temperature and pressure reducer is provided. However, the existing cogeneration unit has high parameters, large capacity and long heat supply period, the high-parameter temperature-reducing pressure reducer can generate the phenomena of thermal fatigue, multi-thermal oxidation, corrosion and the like, and particularly the safety problem exists in the outlet pipeline of the high-parameter temperature-reducing pressure reducer in the design and installation process.
Because the water spray evaporation can cause the wall surface of the downstream pipeline of the temperature and pressure reducer to be heated unevenly, a distance pipeline is generally reserved in the design, and the pipeline is a liquid drop evaporation section and has stronger thermal stress resistance. In the general design of temperature and pressure reducing device pipeline installation, a manufacturer can determine the length of a liquid drop evaporation section pipeline according to the standard when a cogeneration unit operates under the rated working condition. However, the cogeneration unit is often operated under variable working conditions, and particularly during the heating period, the bypass heating load is increased sharply, so that the evaporation length of the liquid drops is changed, and the original design length of the liquid drop evaporation section pipeline is not suitable for the bypass heating operation of the cogeneration unit. Finally, the fatigue damage of the pipeline at the liquid drop evaporation section of the temperature and pressure reducer is caused, and even accidents such as pipeline breakage and the like occur. For different operating environments and pipeline structure parameters, the evaporation lengths of liquid drops are different, and the pipeline of the liquid drop evaporation section of the temperature and pressure reducer must be redesigned in the process of flexibility transformation of the cogeneration unit. In addition, in the running process of the cogeneration unit, effective reference information can be provided for the water spraying control of the temperature and pressure reducer by accurately estimating the length of the liquid drop evaporation section. However, the existing research on the length of the droplet evaporation section of the temperature and pressure reducer is less, and part of experimental analysis does not provide an accurate calculation theory and method for the length of the droplet evaporation section, so that the application of the temperature and pressure reducer in the flexibility modification of the cogeneration unit has a larger safety problem and technical obstacle.
Therefore, a method capable of accurately calculating the length of the evaporation length of the liquid drop of the temperature and pressure reducer is required, the method has certain universal applicability, the evaporation length of the liquid drop can be calculated according to parameters such as steam flow, pipeline diameter and water spraying in the installation design of the temperature and pressure reducer, the change of the evaporation length of the liquid drop can be calculated in real time according to the change of the flow and water spraying parameters in the bypass heat supply operation, and the technical guarantee is provided for the safe operation of the pipeline of the temperature and pressure reducer in the bypass heat supply.
Disclosure of Invention
Aiming at the safety problem of pipeline damage of the evaporation section of the bypass heat supply and temperature reduction pressure reducer at present, the invention aims to provide a method for determining the length of the evaporation section of the liquid drop of the temperature reduction pressure reducer for bypass heat supply of the thermal power generating unit, which contains modeling simulation and regression orthogonal analysis as contents, is scientific and reasonable, has strong applicability and high calculation precision.
The technical scheme for realizing the purpose of the invention is as follows: a method for determining the length of a liquid drop evaporation section of a temperature and pressure reducer for bypass heating of a thermal power generating unit is characterized by comprising the following steps of: it comprises the following contents:
1) Physical model selection and construction of temperature and pressure reducer and liquid drop evaporation section pipeline
Before numerical simulation, related calculation parameters are selected according to different models of the temperature and pressure reducers and the installation schemes to be adopted, wherein a basin model for numerical simulation is mainly established according to the structural parameters of the temperature and pressure reducers:
(1) extracting relevant structural parameters aiming at the calculated temperature and pressure reducer and the liquid drop evaporation section pipeline, and mainly comprising the following steps of: the size of the temperature and pressure reducer valve body, the diameter of the temperature and pressure reducer inlet, the diameter of the temperature and pressure reducer outlet, the diameter of the liquid drop evaporation section pipeline, the diameter of the primary throttle orifice plate, the inner diameter of the primary throttle orifice plate, the diameter of the secondary throttle orifice plate, the inner diameter of the secondary throttle orifice plate, the diameter of the tertiary throttle orifice plate, the inner diameter of the tertiary throttle orifice plate and the diameter of the water spraying valve port;
(2) building a temperature and pressure reducer and a physical mapping point of a liquid drop evaporation section pipeline in GAMBIT modeling software according to the selected parameters, and constructing a three-dimensional basin model of the temperature and pressure reducer and the liquid drop evaporation section pipeline through point connecting lines, line surfaces, surface enclosing bodies and Boolean cut body operations;
2) Three-dimensional basin calculation of temperature and pressure reducers and liquid drop evaporation section pipelines
(1) Outputting the invention piece by the three-dimensional basin model established in the STEP 1) in a STEP format, importing ANSYS ICEM grid division software, naming boundaries of the basin models of the temperature and pressure reducer and the liquid drop evaporation section pipeline, and respectively naming an INLET of the temperature and pressure reducer, an OUTLET of the temperature and pressure reducer and a water spraying valve port as INLET, OUTLET and WATER INLET;
(2) adopting a global grid division method to perform discrete division on the watershed, wherein the grid near the wall surface is encrypted to ensure that the Y + value is within 30, and the SLOW TRANSITION is adopted in the TRANSITION of the unstructured grid to ensure that the grid has smaller distortion rate and better grid quality;
(3) leading a temperature and pressure reducer and a liquid drop evaporation section pipeline grid model into a CFX-PRE, respectively setting an inlet and outlet boundary according to selected steam pressure and temperature parameters, selecting a standard k-epsilon turbulence model to solve a three-dimensional basin, wherein steam in the temperature and pressure reducer and the liquid drop evaporation section pipeline has compressibility and viscosity, and a flow control equation mainly comprises:
continuity equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; u is a velocity vector.
The momentum equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; μ as kinetic viscosity, N $/m 2 (ii) a u, v and w are the components of the velocity vector u in the x, y and z directions; s u 、S v And S w Being the generalized source term of the conservation of momentum equation,
energy equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; t is temperature, DEG C; c k Is the constant temperature heat transfer coefficient of the fluid, W/m 2 ﹒℃；C p Is the constant pressure heat transfer coefficient of the fluid, W/m 2 ﹒℃；S T Is a viscous dissipation term;
(4) and establishing a water spraying temperature-reducing vapor-liquid two-phase flow model, and setting temperature-reducing water parameters according to the water supply temperature and the pressure. The high-temperature high-pressure steam and the desuperheating water drops are evaporated or condensed according to the temperature and the critical point parameters of the high-temperature high-pressure steam and the desuperheating water drops, and the specific mathematical process of the condensation-evaporation multiphase medium model in the CFX is as follows:
the boiling point of the fluid is the relationship between the evaporation pressure and the temperature, and is expressed by the formula (6):
in the formula: p is a radical of v Is the evaporation pressure, pa; p is a radical of s Is the pressure scale, pa; t is p Steam temperature, deg.C; a is a state constant; b is the enthalpy coefficient of steam; c is a temperature coefficient;
when the temperature of the water drops is higher than the boiling point, the mass transfer is represented by the formula (7):
in the formula: m is p Mass of the particles, kg; t is time, s; q C J, convective heat transfer; q R Is the radiant heat exchange quantity, J; l is latent heat of vaporization, J/kg;
when the temperature of the water drops is lower than the boiling point, the mass transfer is represented by the formula (8):
in the formula: dm p Kg for drop mass change; t is time, s; d p Is the particle diameter, m; rho D is a kinetic diffusion coefficient; sh is the Sherwood coefficient; w is a c Is the molecular weight of the vapor; w is a g Is the molecular weight of the mixture; x is the number of s v Equilibrium steam mole fraction; x is the number of v v Is the mole fraction of the mixed gas;
the continuous fluid mass source is represented by the equation (9):
in the formula: dm p Kg for drop mass change; t is time, s; s is a mass source, kg;
meanwhile, convection heat transfer and radiation heat transfer are considered in the working medium heat transfer process, and the heat transfer property is set as fluid dependent by combining the characteristics of the working medium;
(5) starting a CFX-SLOVER solver, calculating the temperature and pressure reducer and the three-dimensional flow field of the liquid drop evaporation section pipeline in parallel by using a single machine, and when the calculated residual reaches 10 -4 Stopping calculation, and extracting the evaporation path and length of the liquid drop;
3) Regression orthogonal analysis of temperature and pressure reducers and liquid drop evaporation section pipelines
(1) Considering that the steam flow and the atomization degree of the sprayed water can seriously affect the liquid drop evaporation effect when the temperature and pressure reducer operates, the change parameters mainly considered in the calculation of the length of the liquid drop evaporation pipeline of the temperature and pressure reducer are the load flow of the temperature and pressure reducer, the particle size of the sprayed water and the outlet pipe diameter of the temperature and pressure reducer;
(2) the method adopts a three-factor quadratic regression orthogonal implementation method, determines the variation range of three control parameters of the temperature and pressure reducer according to the general principle of the installation design of the temperature and pressure reducer, and determines the load flow x 1 Water spray particle diameter x 2 Outlet pipe diameter x 3 For the main study parameters, let x j For each factor of the regression orthogonal analysis, j =1,2,3.x is the number of 1j 、x 2j Upper and lower limits of the factor, respectively, the zero level x of the factor 0j ＝(x 1j +x 2j )/2；
(3) Obtaining a horizontal coding table based on the variation range of each factor, selecting a limited number of calculation points in the reasonable variation range of the factor by regression orthogonal analysis to arrange simulation calculation statistics, establishing a regression equation with certain reliability by virtue of the limited number of calculation points, estimating the length of a corresponding evaporation section by utilizing the regression equation after each structural parameter is determined, and repeating the step 1) and the step 2) according to the established three-factor quadratic regression orthogonal analysis scheme to respectively extract the evaporation path and the length of the liquid drop in each simulation working condition so as to perfect the regression orthogonal analysis index value;
the number of numerical simulations of the analysis protocol is determined by equation (10),
n＝m 0 +m c +m r (10)
in the formula: m is 0 Taking 1 as the central test frequency; m is a unit of c Number of horizontal tests, m c ＝2 p-1 ；m r For asterisk test, m r =2p; p is the number of factors, p =4; arm length of asterisk
The variation interval of the test level can be determined by the upper limit and the lower limit of the factors and the arm length of the asterisk,
in the formula: x is the number of 1j 、x 2j Upper and lower limits for the factors, respectively; r is the arm length of the asterisk;
in the regression orthogonal analysis, all factors should keep consistent dimensions and should not differ too much, and the natural variables of all factors need to be centrally processed, and z is set j For the code value obtained after centralization of the level values of the factors, then there is z j ＝(x j -x 0j )/Δ j ，
The squared difference and the regression coefficient are calculated as (12) formula- (17):
S j ＝B j b j (15)
in the formula: d ij The square sum of each item of the investigation index; z is a radical of ij Centering the encoded value for the interactive item; y is ij Obtaining each investigation index by numerical simulation; b is ij The regression sums of all indexes are considered; b is a mixture of ij Each regression coefficient is taken as a reference value; s j Is a regression sum of squares; f j Is a regression coefficient check term; f. of j Is the degree of freedom of a regression term; s e Is the sum of squares of errors f e Is the error term degree of freedom; y is 0j As the central test value;
the average value of the investigation indexes is; subscript j is the number of the main study factors; subscript i is the serial number of the simulation working condition, and 1, …, n is taken.
4) Significance and loss of similarity testing of regression equations
(1) For analyzing the effectiveness of regression analysis after centralization treatment, each influence factor and investigation index need to be subjected to significance analysis, and the significance analysis is carried out by checking equation regression coefficient, b j 、b ij 、b jj Determines the degree to which it affects the survey index, wherein i =0, b 0 Constant term, i = j, b jj For quadratic terms, i ≠ j, b ij Is an interactive item.
(2) According to the significance test formula of the regression orthogonal test:
in the formula: s h Is the sum of squares of regression terms; f. of h Is the total degree of freedom of the regression term; s R Is the sum of the squares of the remaining terms; f. of R Is the remaining item total degree of freedom; f 0.01 Is a normal distribution 0.01 horizontal value;
the significance test that the equation accords with the ternary-quadratic regression orthogonality is obtained, and the confidence coefficient of the established regression equation is (1-alpha) × 100% =99%, and the significance is achieved under the level of alpha = 0.01;
(3) according to the mismatching test formula:
in the formula: s lf Is the sum of squares of the mismatching terms; f. of lf The total degree of freedom of the simulation loss item; s e Is the sum of the squares of the error terms; f. of e Is the degree of freedom of the error term; f 0.25 Is a normal distribution 0.25 level value;
the established regression equation can be determined to have good invariance, which shows that the evaporation section length has good fitting with the primary term, the interactive term and the secondary term of each factor, has no obvious relation with the higher-order term of each factor,
(4) the regression equation of the corresponding code is obtained by the calculation method and the data processing:
in the calculation of the evaporation length of the liquid drops of the temperature and pressure reducer, the selected parameters are substituted into the formula (20) to obtain the predicted evaporation length.
The invention provides a method for determining the length of a droplet evaporation section of a temperature and pressure reducer for bypass heat supply of a thermal power generating unit, which is based on the following conception:
(1) the bypass heating system of the cogeneration unit is often operated at a non-rated load, and in order to meet the heating demand, the temperature and pressure reducer and the piping system thereof are often in a severe working environment. The water spray temperature reduction system in the temperature reduction pressure reducer can cause the downstream pipeline to be in a non-uniform heating state, so that stress fatigue and even breakage are caused. The original design pipeline is not suitable for the bypass heating system after transformation, however, the current research does not provide the calculation about the length of the liquid drop evaporation section pipeline of the temperature and pressure reducer, so that the length of the special pipeline can not be quantitatively determined in the bypass heating transformation of the combined heat and power generation unit, and certain technical obstacles exist. In addition, the water spraying system is slow in regulation and control and long in reaction time in the bypass heat supply operation, so that the control inertia of the bypass system is large. Therefore, a method for calculating the length of the pipeline of the droplet evaporation section of the temperature and pressure reducer under the influence of various factors is needed. On the one hand, in the design of bypass heat supply reconstruction, the length of the evaporation section of the temperature and pressure reducer can be calculated according to the design requirements of load flow, water spray particle size, outlet pipe diameter of the temperature and pressure reducer and the like, and theoretical standard is provided for construction. On the other hand, the flow length of the liquid drops can be calculated in real time according to the load flow and the water spraying particle size in the bypass heat supply operation, and feedback information is provided for regulating and controlling the water spraying temperature reduction system.
(2) The invention adopts modeling simulation and regression orthogonal analysis method, and calculates the flow path and length of liquid drop in the pipeline of the temperature and pressure reducer under the action of different influence factors through numerical simulation. The internal flow fields of the temperature and pressure reducer and the liquid drop evaporation section pipeline are solved through CFX, the heat exchange, evaporation and vapor-liquid interference processes of high-temperature high-pressure steam and water spray liquid drops and the turbulence of high-speed fluid in the flowing process are fully considered, and the length of the pipeline required by liquid drop evaporation can be accurately calculated.
(3) The CFX is used as a solving tool, the path length of the liquid drop evaporation is used as an investigation index, the quantitative change of the liquid drop evaporation length along with the load flow, the water spraying particle size and the outlet pipe diameter can be obtained through a small amount of distributed simulation working conditions according to hypercube sampling calculation, variance analysis and regression fitting of orthogonal regression analysis, and the interaction influence of multiple factors is considered. And establishing a regression equation of each influence factor and the investigation index, and ensuring the calculation precision of the regression equation after the regression equation is checked. When in use, the required index can be obtained by only solving the regression equation, thereby avoiding the complexity and independence of the experiment calculation of the length of the pipeline at the liquid drop evaporation section of the temperature and pressure reducer and the hysteresis in the control process of the water spraying system.
Compared with the prior art, the invention has the following beneficial technical effects:
the method for determining the length of the droplet evaporation section of the temperature and pressure reducer for bypass heat supply of the thermal power generating unit adopts the combination of modeling simulation and regression orthogonal analysis to establish a regression equation for calculating the length of the droplet evaporation section of the temperature and pressure reducer, can directly calculate the length of the droplet evaporation section through preselected load flow, water spray particle size and outlet pipe diameter parameters, does not need experimental determination, and has the characteristics of simplicity, convenience and accuracy. In addition, the regression equation fitted by the method can monitor the change of the water spraying temperature reduction effect along with the bypass load flow in real time, provide feedback information for a water spraying temperature reduction control system and improve the adjustment performance of the system.
The method can be widely applied to various bypass temperature and pressure reduction systems, only one set of modeling simulation and regression orthogonal analysis is needed for each type of temperature and pressure reduction device, the obtained regression equation can be repeatedly used in subsequent application, multiple correction and check are not needed, and the method has high applicability and accuracy.
The method solves the problem that the length of the droplet evaporation section of the temperature and pressure reducer in the transformation of the bypass heating system of the current cogeneration unit cannot be calculated. The method provides reliable theoretical guidance and construction standards for flexibility modification of the cogeneration unit, and fills the blank in the field of pipeline safety of the temperature and pressure reducing system in bypass heat supply modification. The method is scientific and reasonable, high in applicability, high in calculation precision and good in effect.
Drawings
FIG. 1 is a schematic flow chart of a method for determining the length of a droplet evaporation section of a temperature and pressure reducer for bypass heating of a thermal power generating unit;
FIG. 2 is a schematic structural view of a high-parameter temperature and pressure reducer;
FIG. 3 is a schematic diagram of three-dimensional simulation of the temperature and pressure reducer;
Detailed Description
The invention will be further explained by combining the attached drawings and an embodiment of a certain type of temperature and pressure reducer.
Referring to fig. 1 to 3, the method for determining the length of the droplet evaporation section of the temperature and pressure reducer for bypass heat supply of the thermal power generating unit of the invention comprises the following steps:
(a) Physical model selection and construction link of temperature and pressure reducing device and liquid drop evaporation section pipeline
Before numerical simulation, related calculation parameters are selected according to different models of the temperature and pressure reducers and the installation schemes to be adopted, wherein a basin model for numerical simulation is mainly established according to the structural parameters of the temperature and pressure reducers:
1) Extracting relevant structural parameters aiming at the calculated temperature and pressure reducer and the liquid drop evaporation section pipeline, and mainly comprising the following steps of: the size of the temperature and pressure reducer valve body, the diameter of the temperature and pressure reducer inlet, the diameter of the temperature and pressure reducer outlet, the diameter of the liquid drop evaporation section pipeline, the diameter of the primary throttle orifice plate, the inner diameter of the primary throttle orifice plate, the diameter of the secondary throttle orifice plate, the inner diameter of the secondary throttle orifice plate, the diameter of the tertiary throttle orifice plate, the inner diameter of the tertiary throttle orifice plate and the diameter of the water spraying valve port;
2) Establishing entity mapping points of the temperature and pressure reducer and the liquid drop evaporation section pipeline in GAMBIT modeling software according to the selected parameters, and constructing a three-dimensional basin model of the temperature and pressure reducer and the liquid drop evaporation section pipeline through operations such as point connecting lines, line surfaces, plane dimension bodies, boolean cut bodies and the like; the GAMBIT modeling software is a commercially available product familiar to those skilled in the art.
(b) Three-dimensional basin calculation link of temperature and pressure reducer and liquid drop evaporation section pipeline
1) Outputting the invention piece from the three-dimensional basin model established in the STEP (a) in a STEP format, and importing the invention piece into ANSYS ICEM mesh division software. Carrying out boundary naming on a temperature and pressure reducer and a basin model of a liquid drop evaporation section pipeline, and respectively naming an INLET of the temperature and pressure reducer, an OUTLET of the temperature and pressure reducer and a water spraying valve port as INLET, OUTLET and WATER INLET;
2) Carrying out discrete division on the watershed by adopting a global grid division method, wherein the grid on the near wall surface is encrypted, the Y + value is ensured to be within 30, and the SLOW TRANSITION is adopted for the TRANSITION of the non-structural grid, so that the grid has smaller distortion rate and better grid quality;
3) Introducing the temperature and pressure reducer and the liquid drop evaporation section pipeline grid model into a CFX-PRE, respectively setting the inlet and outlet boundaries according to the selected steam pressure and temperature parameters, and solving a three-dimensional basin by using a standard k-epsilon turbulence model; the steam in the temperature and pressure reducer and the liquid drop evaporation section pipeline has compressibility and viscosity, and the flow control equation mainly comprises:
continuity equation:
in the formula: rho is fluid density, kg/m 3 (ii) a t is time, s; u is a velocity vector.
The momentum equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; μ as kinetic viscosity, N $/m 2 (ii) a u, v and w are the components of the velocity vector u in the x, y and z directions; s u 、S v And S w Being the generalized source term of the conservation of momentum equation,
energy equation:
in the formula: rho is fluid density, kg/m 3 (ii) a t is time, s; t is temperature, DEG C; c k Is the constant temperature heat transfer coefficient of the fluid, W/m 2 ﹒℃；C p Is the constant pressure heat transfer coefficient of the fluid, W/m 2 ﹒℃；S T Is a viscous dissipation term;
4) And establishing a water spraying temperature-reducing vapor-liquid two-phase flow model, and setting temperature-reducing water parameters according to the water supply temperature and pressure. The high-temperature high-pressure steam and the temperature-reducing water drops are evaporated or condensed according to the temperature and the critical point parameters of the high-temperature high-pressure steam and the temperature-reducing water drops. The concrete mathematical process of the condensation-evaporation multi-phase medium model in the CFX is as follows:
the boiling point of the fluid is the relationship between evaporation pressure and temperature, and is expressed by the formula (6):
in the formula: p is a radical of v Is the evaporation pressure, pa; p is a radical of formula s Is the pressure scale, pa; t is p Steam temperature, deg.C; a is a state constant; b is the enthalpy coefficient of steam; c is a temperature coefficient;
when the temperature of the water drops is higher than the boiling point, the mass transfer is represented by the formula (7):
in the formula: m is a unit of p Mass of the particles, kg; t is time, s; q C J, convective heat transfer; q R Is the radiant heat exchange quantity, J; l is latent heat of vaporization, J/kg;
when the temperature of the water drops is lower than the boiling point, the mass transfer is represented by the formula (8):
in the formula: dm p Kg for drop mass change; t is time, s; d is a radical of p Is the particle diameter, m; rho D is a kinetic diffusion coefficient; sh is Sherwood coefficient; w is a c Is the molecular weight of the vapor; w is a g Is the molecular weight of the mixture; x is the number of s v Equilibrium steam mole fraction; x is the number of v v Is the mixed gas mole fraction;
the continuous fluid mass source may be represented by the equation (9):
in the formula: dm p Kg for drop mass change; t is time, s; s is a mass source, kg;
meanwhile, the heat transfer process of the working medium considers the convection heat transfer and the radiation heat transfer, the heat transfer property is set as the fluid dependent by combining the self characteristic of the working medium,
5) Starting a CFX-SLOVER solver, calculating the temperature and pressure reducer and the three-dimensional flow field of the liquid drop evaporation section pipeline in parallel by using a single machine, and when the calculated residual reaches 10 -4 Stopping calculation, and extracting the evaporation path and length of the liquid drop;
(c) Regression orthogonal analysis link of temperature and pressure reducer and liquid drop evaporation section pipeline
1) Considering that the steam flow and the atomization degree of the sprayed water can seriously affect the liquid drop evaporation effect when the temperature and pressure reducer operates, the change parameters mainly considered in the calculation of the length of the liquid drop evaporation pipeline of the temperature and pressure reducer are the load flow of the temperature and pressure reducer, the particle size of the sprayed water and the outlet pipe diameter of the temperature and pressure reducer;
2) The method adopts a three-factor quadratic regression orthogonal implementation method, determines the variation range of three control parameters of the temperature and pressure reducer according to the general principle of the installation design of the temperature and pressure reducer, and determines the load flow x 1 And the water spray particle diameter x 2 Outlet pipe diameter x 3 Are the main research parameters. Let x j For each factor of the regression orthogonal analysis, j =1,2,3.x is a radical of a fluorine atom 1j 、x 2j Upper and lower limits of the factor, respectively, the zero level x of the factor 0j ＝(x 1j +x 2j )/2；
3) Obtaining a horizontal coding table based on the variation range of each factor, selecting a limited number of calculation points in the reasonable variation range of the factors for analog calculation statistics by regression orthogonal analysis, establishing a regression equation with certain reliability by virtue of the limited number of calculation points, estimating the length of a corresponding evaporation section by utilizing the regression equation after each structural parameter is determined, repeating the step (a) and the step (b) according to the established three-factor quadratic regression orthogonal analysis scheme, respectively extracting the evaporation path and length of liquid drops in each simulation working condition, and perfecting the regression orthogonal analysis index value;
the number of numerical simulations of the analysis solution can be determined from equation (10),
n＝m 0 +m c +m r (10)
in the formula: m is 0 Taking 1 as the central test frequency; m is c Number of two horizontal tests, m c ＝2 p-1 ；m r For asterisk test, m r =2p; p is the number of factors, p =4; arm length of asterisk
The variation interval of the test level can be determined by the upper limit and the lower limit of the factors and the arm length of the asterisk,
in the formula: x is a radical of a fluorine atom 1j 、x 2j Upper and lower limits for the factors, respectively; r is arm length of asterisk.
In the regression orthogonal analysis, all factors should keep consistent dimensions and should not differ too much, and the natural variables of all factors need to be centrally processed, and z is set j For the code value obtained after centralization of the level values of the factors, then there is z j ＝(x j -x 0j )/Δ j 。
The squared difference and the regression coefficient are calculated as (12) formula- (17) formula:
S j ＝B j b j (15)
in the formula: d ij The square sum of each item of the investigation index; z is a radical of ij Centering the encoded value for the interactive item; y is ij Obtaining each investigation index by numerical simulation; b is ij The regression sum of each item of the investigation index; b ij Each regression coefficient is taken as the index; s j Is a regression sum of squares; f j Is a regression coefficient check term; f. of j Is the degree of freedom of a regression term; s e Is the sum of squares of errors f e Is the degree of freedom of the error term; y is 0j As the central test value;
the average value of the investigation indexes is; subscript j is the number of the main study factors; subscript i is the serial number of the simulation working condition, and 1, …, n is taken.
(d) Significance and mismatching detection link of regression equation
1) For the analysis of the effectiveness of the regression analysis after the centering treatment, the significance of the influencing factors and the investigation indexes is analyzed, and the equation regression coefficient is checked, b j 、b ij 、b jj Determines the degree to which it affects the index under investigation, where i =0, b 0 Constant term, i = j, b jj For quadratic terms, i ≠ j, b ij Is an interactive item.
2) According to the significance test formula of the regression orthogonal test:
in the formula: s. the h Is the sum of squares of regression terms; f. of h Is the total degree of freedom of the regression term; s R Is the sum of the squares of the remaining terms; f. of R Is the remaining item total degree of freedom; f 0.01 Is a normal distribution 0.01 horizontal value;
the significance test that the equation accords with the ternary-quadratic regression orthogonality is obtained, and the confidence coefficient of the established regression equation is (1-alpha) × 100% =99%, and the significance is achieved under the level of alpha = 0.01;
3) According to the mismatching test formula:
in the formula: s. the lf Is the sum of squares of the mismatching terms; f. of lf The total degree of freedom of the simulation loss item; s. the e Is the sum of the squares of the error terms; f. of e Is the degree of freedom of the error term; f 0.25 Is a normal distribution 0.25 level value;
the established regression equation can be determined to have good invariance, which shows that the evaporation section length has good fitting with the primary term, the interactive term and the secondary term of each factor, has no obvious relation with the higher-order term of each factor,
4) Obtaining a regression equation of the corresponding code by the calculation method and data processing:
in the calculation of the evaporation length of the liquid drops of the temperature and pressure reducer, the selected parameters are substituted into the formula (22) to obtain the predicted evaporation length.
Calculation example:
as shown in fig. 1, example calculation is now performed for the above specific embodiment, taking a C1Z604-0 integrated temperature and pressure reducer in a bypass system of a certain 300MW unit as an example, the specific steps are as follows:
(a) Physical model selection and construction of temperature and pressure reducer and liquid drop evaporation section pipeline
The structural parameters and the physical model of the temperature and pressure reducer are shown in FIG. 2. Orifice parameters are shown in table 1.
TABLE 1 part names and parameters
Building the entity mapping points of the temperature and pressure reducer and the liquid drop evaporation section pipeline in GAMBIT modeling software according to the selected parameters, and building a three-dimensional basin model of the temperature and pressure reducer and the liquid drop evaporation section pipeline through operations such as point connecting lines, line surfaces, plane dimension bodies, boolean cut bodies and the like, wherein the built model is shown in figure 3.
(b) Three-dimensional basin calculation of temperature and pressure reduction device and liquid drop evaporation section pipeline
Introducing a temperature and pressure reducer and a droplet evaporation section pipeline grid model into a CFX-PRE, respectively setting an inlet and outlet boundary according to selected steam pressure and temperature parameters, selecting a standard k-epsilon turbulence model to solve a three-dimensional basin, wherein the steam in the temperature and pressure reducer and the droplet evaporation section pipeline has compressibility and viscosity, and a flow control equation mainly comprises the following steps:
continuity equation:
in the formula: rho is fluid density, kg/m 3 (ii) a t is time, s; u is a velocity vector.
The momentum equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; μ as kinetic viscosity, N $/m 2 (ii) a u, v and w are the components of the velocity vector u in the x, y and z directions; s u 、S v And S w Being the generalized source term of the conservation of momentum equation,
energy equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; t is temperature, DEG C; c k Is the constant temperature heat transfer coefficient of the fluid, W/m 2 ﹒℃；C p Is the constant pressure heat transfer coefficient of the fluid, W/m 2 ﹒℃；S T Is a viscous dissipation term;
the high-temperature high-pressure steam and the desuperheating water drops are evaporated or condensed according to the temperature and the critical point parameters of the high-temperature high-pressure steam and the desuperheating water drops, and the specific mathematical process of the condensation-evaporation multiphase medium model in the CFX is as follows:
the boiling point of the fluid is the relationship between evaporation pressure and temperature, and is expressed by the formula (6):
in the formula: p is a radical of v Is the evaporation pressure, pa; p is a radical of formula s Is the pressure scale, pa; t is a unit of p Steam temperature, deg.C; a is a state constant; b is the enthalpy coefficient of steam; c is a temperature coefficient;
when the temperature of the water drops is higher than the boiling point, the mass transfer is represented by the formula (7):
in the formula: m is p Mass of the particles, kg; t is time, s; q C J, convective heat transfer; q R Is the radiant heat exchange quantity, J; l is latent heat of vaporization, J/kg;
when the temperature of the water drops is lower than the boiling point, the mass transfer (8) is as follows:
in the formula: dm p Kg for drop mass change; t is time, s; d is a radical of p Is the particle diameter, m; rho D is a kinetic diffusion coefficient; sh is the Sherwood coefficient; w is a c Is the molecular weight of the vapor; w is a g Is the mixture molecular weight; x is the number of s v Equilibrium steam mole fraction; x is the number of v v Is the mole fraction of the mixed gas;
the continuous fluid mass source may be represented by the equation (9):
in the formula: dm p Kg for drop mass change; t is time, s; s is a mass source, kg;
meanwhile, convection heat transfer and radiation heat transfer are considered in the working medium heat transfer process, and the heat transfer property is set as fluid dependent by combining the characteristics of the working medium;
adopting a CFX-SLOVER solver and a single machine to calculate the three-dimensional flow field of the temperature and pressure reducing device and the liquid drop evaporation section pipeline in parallel, and when the calculation residual reaches 10 -4 Stopping calculation, and extracting the evaporation path and length of the liquid drop;
(c) Regression orthogonal analysis of temperature and pressure reducers and liquid drop evaporation section pipelines
The variation range of three control parameters of the temperature and pressure reducing device is determined according to the general principle of the installation design of the temperature and pressure reducing device: load flow x 1 Is 110 to 330t/h; water spray particle size x 2 0.01-0.15mm; outlet pipe diameter x 3 Is 200-500mm. Let x j For each factor of the regression orthogonal analysis, j =1,2,3.x is the number of 1j 、x 2j Respectively the upper and lower limits of the factor,zero level x of the factor 0j ＝(x 1j +x 2j )/2. The horizontal codes obtained based on the variation range of each factor are shown in table 2;
TABLE 2 two-level four-factor (1/2 implementation) level coding table
The numerical simulation number of the analysis scheme can be determined by the formula (10), and is 17 simulation working conditions,
n＝m 0 +m c +m r (10)
in the formula: m is 0 Taking 3 as the central test times; m is a unit of c Number of two horizontal tests, m c ＝2 p-1 ；m r For the asterisk test, m r =2p; p is the number of factors, p =4; arm length of asterisk
I.e. r =1.353;
the variation interval of the test level can be determined by the upper limit and the lower limit of the factors and the arm length of the asterisk,
in the formula: x is a radical of a fluorine atom 1j 、x 2j Upper and lower limits for the factors, respectively; r is the arm length of the asterisk;
in the regression orthogonal analysis, all factors should keep consistent dimensions and should not differ too much, and the natural variables of all factors need to be centrally processed. Let z j For the code value obtained after centralization of the level values of the factors, then there is z j ＝(x j -x 0j )/Δ j ；
The squared difference and the regression coefficient are calculated as (12) formula- (17) formula:
S j ＝B j b j (15)
in the formula: d ij The square sum of each item of the investigation index; z is a radical of ij Centering the encoded value for the interactive item; y is ij Obtaining each investigation index by numerical simulation; b is ij The regression sums of all indexes are considered; b ij Each regression coefficient is taken as a reference value; s j Is a regression sum of squares; f j Is a regression coefficient check term; f. of j Is the degree of freedom of a regression term; s. the e Is the sum of squares of errors f e Is the degree of freedom of the error term; y is 0j As the central test value;
the average value of the investigation indexes is; subscript j is the number of the main study factors; subscript i is the serial number of the simulation working condition, and 1, …, n is taken.
(d) Significance and instability inspection link of regression equation
1) For analyzing the effectiveness of regression analysis after centralization treatment, each influence factor and investigation index need to be subjected to significance analysis, and the significance analysis is carried out by checking equation regression coefficient, b j 、b ij 、b jj Determines the degree to which it affects the index under investigation, where i =0, b 0 Is a constant term, i = j, b jj For quadratic terms, i ≠ j, b ij Is an interactive item.
Repeating the steps (a) and (b) according to the arrangement of regression orthogonal analysis, and finally obtaining the calculation result and analysis of the regression analysis as shown in Table 3;
TABLE 3 ternary quadratic regression orthogonal test result analysis and calculation table
(d) Significance and instability inspection link of regression equation
To perform significance and uncertainty tests on the regression equation, 3 center tests will be performed, the y of which 0j (j =1,2,3) are 3.5, 3.75, 3.9, respectively, giving the sum of the squared errors S e =0.0082 and degree of freedom f thereof e =2, determining the coefficients of the regression equation by regression coefficient testing in an orthogonal test when F j Satisfies F j ＞F 0.25 (f j ,f e ) It can be considered that the factor corresponding to y has a significant influence on y. In the table ". Sup." indicates that the significance thereof satisfies F 0.25 (f j ,f e ) Horizontal, i.e. confidence reaches α =0.25; by the same token, significance was achieved to F 0.05 (f j ,f e ) (ii) a ". Indicates that significance reached F 0.01 (f j ,f e ). Except that b 1 、b 12 And b 22 Corresponding F j ＜F 0.25 (f j ,f e ) Besides, the regression coefficients of other terms have better significance, and the non-significant regression terms are put into the residual terms to obtain the residual square sum S R ＝S-S h =1.44, while obtaining the misleading square sum S lf ＝S h -S e =1.359. Wherein S is the sum of the total squares,
from b j 、b ij 、b jj The degree of influence on the investigation index is determined as follows: the first term is z 2 >z 3 >z 1 (ii) a The interactive item is z 23 >z 13 >z 12 ；
According to the significance test formula of the regression orthogonal test:
the significance test that the equation accords with the ternary-quadratic regression orthogonality is obtained, and the confidence coefficient of the established regression equation is (1-alpha) × 100% =99%, and the significance is achieved under the level of alpha = 0.01;
similarly, according to the mismatching test formula:
the regression equation established by the invention can be determined to have good invariance, which shows that the evaporation section length has good fitting with the primary term, the interactive term and the secondary term of each factor, has no obvious relation with the higher-order term of each factor,
the regression equation of the corresponding code can be obtained by the calculation method and the data processing:
based on test verification and optimization design, the codes of the regression equation need to be converted into natural variables, and the test codes are subjected to inverse centralization processing according to a centralization processing formula so that the equation becomes x-related j As a function of (a) or (b),
in the using process, the selected parameters are brought into the formula (21), and then the formula (20) is further brought to obtain the predicted evaporation section length.
In order to verify the accuracy of the regression equation, a group of numerical values is selected within the reasonable range of each factor to carry out theoretical calculation of the formula. Value x 1 ＝330t/h、x 2 ＝0.10mm、x 3 The regression equation is substituted by =380mm to obtain a formula calculation result of 6.6826m, and the error of the formula calculation result and the calculation result of the numerical software CFX is 7.26%. According to the technical rule, the pipeline of the outlet section of the temperature and pressure reducer for the operation parameters is not less than 6.9m. And then, substituting the array with the experimental serial number of 1 into a calculation result, wherein the difference between the array and the original value is 8.25m and 8.5m is 2.94%, which shows that the equation has higher accuracy and meets the requirements of engineering application to a certain extent.
When the method is used, the value selection range of each parameter needs to be noticed as follows: load flow x 1 Is 110 to 330t/h; water spray particle size x 2 0.01-0.15mm; outlet pipe diameter x 3 Is 200-500mm. To estimate values outside this range requires redesigning orthogonal experiments for regression fitting.
While the preferred embodiments of the present invention have been described in detail, it is to be understood that the invention is not limited thereto, and that various equivalent modifications and substitutions may be made by those skilled in the art without departing from the spirit of the present invention and are intended to be included within the scope of the present application.
Claims (1)
1. A method for determining the length of a droplet evaporation section of a temperature and pressure reducer for bypass heat supply of a thermal power generating unit is characterized by comprising the following steps of: it comprises the following contents:
1) Physical model selection and construction of temperature and pressure reducer and liquid drop evaporation section pipeline
Before numerical simulation, related calculation parameters are selected according to different models of the temperature and pressure reducers and the installation schemes to be adopted, wherein a basin model for numerical simulation is mainly established according to the structural parameters of the temperature and pressure reducers:
(1) extracting relevant structural parameters aiming at the calculated temperature and pressure reducer and the liquid drop evaporation section pipeline, and mainly comprising the following steps of: the size of the temperature and pressure reducer valve body, the diameter of the temperature and pressure reducer inlet, the diameter of the temperature and pressure reducer outlet, the diameter of the liquid drop evaporation section pipeline, the diameter of the primary throttle orifice plate, the inner diameter of the primary throttle orifice plate, the diameter of the secondary throttle orifice plate, the inner diameter of the secondary throttle orifice plate, the diameter of the tertiary throttle orifice plate, the inner diameter of the tertiary throttle orifice plate and the diameter of the water spraying valve port;
(2) building a temperature and pressure reducer and a physical mapping point of a liquid drop evaporation section pipeline in GAMBIT modeling software according to the selected parameters, and constructing a three-dimensional basin model of the temperature and pressure reducer and the liquid drop evaporation section pipeline through point connecting lines, line surfaces, surface enclosing bodies and Boolean cut body operations;
2) Three-dimensional basin calculation of temperature and pressure reducers and liquid drop evaporation section pipelines
(1) Outputting a file of the three-dimensional basin model established in the STEP 1) in a STEP format, importing the file into ANSYS ICEM grid division software, naming boundaries of the basin models of the temperature and pressure reducer and the liquid drop evaporation section pipeline, and respectively naming an INLET of the temperature and pressure reducer, an OUTLET of the temperature and pressure reducer and a water spraying valve port as INLET, OUTLET and WATER INLET;
(2) adopting a global grid division method to perform discrete division on the watershed, wherein the grid near the wall surface is encrypted to ensure that the Y + value is within 30, and the SLOW TRANSITION is adopted in the TRANSITION of the unstructured grid to ensure that the grid has smaller distortion rate and better grid quality;
(3) introducing a temperature and pressure reducer and a droplet evaporation section pipeline grid model into a CFX-PRE, respectively setting an inlet and outlet boundary according to selected steam pressure and temperature parameters, selecting a standard k-epsilon turbulence model to solve a three-dimensional basin, wherein the steam in the temperature and pressure reducer and the droplet evaporation section pipeline has compressibility and viscosity, and a flow control equation mainly comprises the following steps:
continuity equation:
in the formula: rho is fluid density, kg/m 3 (ii) a t is time, s; u is a velocity vector.
The momentum equation:
in the formula: rho is the fluid density, kg/m 3 (ii) a t is time, s; μ as kinetic viscosity, N $/m 2 (ii) a u, v and w are the components of the velocity vector u in the x, y and z directions; s u 、S v And S w Being the generalized source term of the conservation of momentum equation,
energy equation:
in the formula: rho is fluid density, kg/m 3 (ii) a t is time, s; t is temperature, DEG C; c k Is the constant temperature heat transfer coefficient of the fluid, W/m 2 ﹒℃；C p Is the constant pressure heat transfer coefficient of the fluid, W/m 2 ﹒℃；S T Is a viscous dissipation term;
(4) and establishing a water spraying temperature-reducing vapor-liquid two-phase flow model, and setting temperature-reducing water parameters according to the water supply temperature and the pressure. The high-temperature high-pressure steam and the desuperheating water drops are evaporated or condensed according to the temperature and the critical point parameters of the high-temperature high-pressure steam and the desuperheating water drops, and the concrete mathematical process of the condensation-evaporation multi-phase medium model in the CFX is as follows:
the boiling point of the fluid is the relationship between the evaporation pressure and the temperature, and is expressed by the formula (6):
in the formula: p is a radical of formula v Is the evaporation pressure, pa; p is a radical of s Is the pressure scale, pa; t is p Steam temperature, deg.C; a is a state constant; b is the enthalpy coefficient of steam; c is a temperature coefficient;
when the temperature of the water drops is higher than the boiling point, the mass transfer is represented by the formula (7):
in the formula: m is p Mass of the particles, kg; t is time, s; q C J, convective heat transfer; q R Is the radiant heat exchange quantity, J; l is latent heat of vaporization, J/kg;
when the temperature of the water drops is lower than the boiling point, the mass transfer is represented by the formula (8):
in the formula: dm p Kg for drop mass change; t is time, s; d p Is the particle diameter, m; rho D is a kinetic diffusion coefficient; sh is the Sherwood coefficient; w is a c Is the molecular weight of the vapor; w is a g Is the molecular weight of the mixture; x is the number of s v Equilibrium steam mole fraction; x is the number of v v Is the mole fraction of the mixed gas;
the continuous fluid mass source is represented by the equation (9):
in the formula: dm p Kg for drop mass change; t is time, s; s is a mass source, kg;
meanwhile, the heat transfer process of the working medium considers the convection heat transfer and the radiation heat transfer, and the heat transfer property is set as the fluid dependent by combining the characteristics of the working medium;
(5) starting a CFX-SLOVER solver, calculating the temperature and pressure reducer and the three-dimensional flow field of the liquid drop evaporation section pipeline in parallel by using a single machine, and when the calculated residual reaches 10 -4 Stopping calculation, and extracting the evaporation path and length of the liquid drop;
3) Regression orthogonal analysis of temperature and pressure reducers and liquid drop evaporation section pipelines
(1) Considering that the steam flow and the atomization degree of the sprayed water can seriously affect the liquid drop evaporation effect when the temperature and pressure reducer operates, the change parameters mainly considered in the calculation of the length of the liquid drop evaporation pipeline of the temperature and pressure reducer are the load flow of the temperature and pressure reducer, the particle size of the sprayed water and the outlet pipe diameter of the temperature and pressure reducer;
(2) the method adopts a three-factor quadratic regression orthogonal implementation method, determines the variation range of three control parameters of the temperature and pressure reducer according to the general principle of the installation design of the temperature and pressure reducer, and determines the load flow x 1 Water spray particle diameter x 2 Outlet pipe diameter x 3 For the main study parameters, let x j For each factor of the regression orthogonal analysis, j =1,2,3.x is a radical of a fluorine atom 1j 、x 2j Upper and lower limits of the factor, respectively, the zero level x of the factor 0j ＝(x 1j +x 2j )/2；
(3) Obtaining a horizontal coding table based on the variation range of each factor, selecting a limited number of calculation points in the reasonable variation range of the factor by regression orthogonal analysis to arrange simulation calculation statistics, establishing a regression equation with certain reliability by virtue of the limited number of calculation points, estimating the length of a corresponding evaporation section by utilizing the regression equation after each structural parameter is determined, and repeating the step 1) and the step 2) according to the established three-factor quadratic regression orthogonal analysis scheme to respectively extract the evaporation path and the length of the liquid drop in each simulation working condition so as to perfect the regression orthogonal analysis index value;
the number of numerical simulations of the analysis solution is determined by equation (10),
n＝m 0 +m c +m r (10)
in the formula: m is 0 Taking 1 as the central test frequency; m is c Number of two horizontal tests, m c ＝2 p-1 ；m r For asterisk test, m r =2p; p is the number of factorsP =4; arm length of asterisk
The variation interval of the test level can be determined by the upper limit and the lower limit of the factors and the arm length of the asterisk,
in the formula: x is a radical of a fluorine atom 1j 、x 2j Upper and lower limits for the factors, respectively; r is the arm length of the asterisk;
in the regression orthogonal analysis, all factors should keep consistent dimensions and should not differ too much, and the natural variables of all factors need to be centrally processed, and z is set j For the code value obtained after centralization of the level values of the factors, then there is z j ＝(x j -x 0j )/Δ j ，
The squared difference and the regression coefficient are calculated as (12) formula- (17):
S j ＝B j b j (15)
in the formula: d ij The square sum of each item of the investigation index; z is a radical of formula ij Centering the encoded value for the interactive item; y is ij Obtaining each investigation index by numerical simulation; b is ij The regression sum of each item of the investigation index; b ij Each regression coefficient is taken as the index; s j Is a regression sum of squares; f j Is a regression coefficient check term; f. of j Is the degree of freedom of a regression term; s e Is the sum of squared errors f e Is the error term degree of freedom; y is 0j As the center test value;
the average value of the investigation indexes is; subscript j is the number of the major study factors; subscript i is the serial number of the simulation working condition, and 1, …, n is taken.
4) Significance and loss of similarity testing of regression equations
(1) For analyzing the effectiveness of regression analysis after centralized processing, significance analysis is required to be carried out on all influence factors and investigation indexes, and the significance analysis is carried out by checking the equation regression coefficient, b j 、b ij 、b jj Determines the degree to which it affects the index under investigation, where i =0, b 0 Constant term, i = j, b jj For quadratic terms, i ≠ j, b ij Is an interactive item.
(2) According to the significance test formula of the regression orthogonal test:
in the formula: s h Is the sum of squares of regression terms; f. of h Is the total degree of freedom of the regression term; s R Is the sum of the squares of the remaining terms; f. of R Is the remaining item total degree of freedom; f 0.01 Is a normal distribution 0.01 horizontal value;
the significance test that the equation accords with the ternary-quadratic regression orthogonality is obtained, and the confidence coefficient of the established regression equation is (1-alpha) × 100% =99%, and the significance is achieved under the level of alpha = 0.01;
(3) according to the mishap test formula:
in the formula: s lf Is the sum of squares of the mismatching terms; f. of lf The total degree of freedom of the simulation loss item; s e Is the sum of the squares of the error terms; f. of e Is the degree of freedom of the error term; f 0.25 Is a normal distribution 0.25 level value;
the established regression equation can be determined to have good invariance, which shows that the length of the evaporation zone has good fitting with the primary term, the interactive term and the secondary term of each factor, has no obvious relation with the higher-order term of each factor,
(4) the regression equation of the corresponding code is obtained by the calculation method and the data processing:
in the calculation of the evaporation length of the liquid drops of the temperature and pressure reducer, the selected parameters are substituted into the formula (20) to obtain the predicted evaporation length.
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